Preheat the oven to 350°F (175°C). Grease and flour a 9x13-inch baking pan.
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt. Set aside.
In a large mixing bowl, combine the granulated sugar, brown sugar, and vegetable oil. Mix until well combined.
Add the eggs, pumpkin puree, and vanilla extract to the sugar mixture. Beat until smooth and creamy.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Be careful not to overmix.
Pour half of the batter into the prepared baking pan. Drizzle half of the caramel sauce over the batter. Pour the remaining batter on top and finish with the rest of the caramel sauce. Use a knife to swirl the caramel into the batter gently.
Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.
Serve warm or at room temperature, drizzling extra caramel sauce on top if desired.